Coherism: A Variational Feedback Framework for Quantum Information and Spacetime Geometry

We propose a variational framework that couples quantum information and spacetime geometry through a single functional of the quantum state and the metric. The central object is a coherence functional, built from (i) the relative entropy of the quantum state with respect to a locally geometry-adapted reference state, (ii) a coarse-grained generalized entropy inside causal diamonds, and (iii) a scale-dependent geometric action. Variation with respect to the metric defines an informational stress tensor that augments the semiclassical Einstein equations, while variation with respect to the quantum state yields a geometry-dependent open-system evolution. We show that this framework reproduces the semiclassical Einstein equation and the Einstein-Langevin form of stochastic gravity in appropriate limits. As a concrete prediction, we derive a small, coherence-dependent violation of the Weak Equivalence Principle for macroscopic quantum superpositions, which may be testable with next-generation atom interferometry. The resulting picture treats gravity and quantum mechanics as complementary limits of a deeper feedback law governing the alignment of quantum information with spacetime geometry.